Question

An oil company has two refineries. Refinery A produces 200 barrels of high-grade oil, 300 barrels of medium-grade oil, and 200 barrels of low-grade oil and costs $12,000 to operate. Each day, Refinery B produces 100 barrels of high-grade oil, 100 barrels of medium-grade oil, and 200 barrels of low-grade oil and costs $10,000 to operate. The company must produce at least 800 barrels of high-grade oil, 900 barrels of medium-grade oil, and 1,000 barrels of low-grade oil. What is the minimum cost to operate both refineries?

Answer 1

$56,000

Explanation:

If x is the number of days that Refinery A is in operation, and y is the number of days that Refinery B is in operation, then:

200x + 100y ≥ 800

300x + 100y ≥ 900

200x + 200y ≥ 1000

The total cost is:

C = 12,000x + 10,000y

x and y must be integers. Possible combinations are:

x = 0, y = 9

x = 1, y = 6

x = 2, y = 4

x = 3, y = 2

x = 4, y = 1

x = 5, y = 0

The costs of these combinations are:

`\left[\begin{array}{ccc}x&y&C\\0&9&\$90,000\\1&6&\$72,000\\2&4&\$64,000\\3&2&\$56,000\\4&1&\$58,000\\5&0&\$60,000\end{array}\right]`

The minimum cost is $56,000.